Somdev, who had become the first Indian to qualify for the French Open in 13 years, lost 2-6 7-6(2) 3-6 to Deheart,who is 114 places below him at 228 in th ATP rankings.
Now Indian hopes to see a players in the singles main draw rest on Prakash Amritraj, who will face Marinko Matosevic in the second round.
However, Somdev is still in contention in the doubles qualifiers as he and his Filipino partner Treat Conrad Huey will take on seventh seeds Prakash and Swiss Yves Allegro.
Meanwhile, Harsh Mankad and his partner Ilija Bozoljac of Serbia, seeded eighth, beat the Brazilian pair of Thiago Alves and Joao Souza 6-3 7-6(5) in the first round.
They face Alexander Peya of Austria and Germany's Bjorn Phau in the second round.